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2016-05-11T12:58:38Z

Created page with "In mathematics, the logarithm is the inverse operation to exponentiation. == Description == That means the logarithm of a number is the expone..."

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In [[mathematics]], the logarithm is the [[Inverse function|inverse operation]] to [[exponentiation]].

== Description ==

That means the logarithm of a number is the [[exponent]] to which another fixed value, the [[Base (exponentiation)|base]], must be raised to produce that number.

In simple cases the logarithm counts repeated [[multiplication]].

The logarithm to base 10 (that is b = 10) is called the [[common logarithm]] and has many applications in [[science]] and [[engineering]].

The [[natural logarithm]] has the number [[e (mathematical constant)|e]] (≈ 2.718) as its base; its use is widespread in [[mathematics]] and [[physics]], because of its simpler derivative.

The [[binary logarithm]] uses base 2 (that is b = 2) and is commonly used in [[computer science]].

Logarithms were introduced by [[John Napier]] in the early 17th century as a means to simplify calculations.

They were rapidly adopted by [[navigators]], [[scientists]], [[engineers]], and others to perform computations more easily, using [[Slide rule|slide rules]] and [[Logarithm table|logarithm tables]].

Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler [[addition]] because of the fact — important in its own right — that the logarithm of a [[Product (mathematics)|product]] is the [[Summation|sum]] of the logarithms of the factors:

\log_b(xy) = \log_b (x) + \log_b (y), \,

provided that b, x and y are all positive and b ≠ 1.

The present-day notion of logarithms comes from [[Leonhard Euler]], who connected them to the [[exponential function]] in the 18th century.

Logarithmic scales reduce wide-ranging quantities to tiny scopes.

For example, the decibel is a unit quantifying signal power log-ratios and amplitude log-ratios (of which sound pressure is a common example).

In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and [[fractals]].

They describe musical intervals, appear in formulas counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting.

In the same way as the logarithm reverses exponentiation, the complex logarithm is the inverse function of the exponential function applied to [[Complex number|complex numbers]].

The [[discrete logarithm]] is another variant; it has uses in [[public-key cryptography]].

== See also ==

* [[Base (exponentiation)]]
* [[Cologarithm]]
* [[Exponential function]]
* [[Exponentiation]]
* [[Decimal exponent]] (dex)
* [[Index of logarithm articles]]
* [[Inverse function]]

== External links ==

* [https://en.wikipedia.org/wiki/Logarithm Logarithm] @ Wikipedia

[[Category:Mathematics]]

Logarithm - Revision history

Karl Jones: Created page with "In mathematics, the logarithm is the inverse operation to exponentiation. == Description == That means the logarithm of a number is the expone..."